# Minimizing the Number of Detrimental Objects in Multi-Dimensional Graph-Based Codes

## TL;DR

This paper introduces a technique to optimize multi-dimensional graph-based codes by reducing detrimental objects, leading to improved error correction and longer lifespan in dense storage systems.

## Contribution

It presents a novel method for minimizing harmful objects in MD codes through strategic relocations, enhancing code performance over traditional cycle-focused approaches.

## Key findings

- Significant lifetime gains in Flash systems using MD codes.
- Effective reduction of detrimental objects compared to cycle-based methods.
- Applicable to various one-dimensional codes.

## Abstract

In order to meet the demands of data-hungry applications, data storage devices are required to be increasingly denser. Various sources of error appear with this increase in density. Multi-dimensional (MD) graph-based codes are capable of mitigating error sources like interference and channel non-uniformity in dense storage devices. Recently, a technique was proposed to enhance the performance of MD spatially-coupled codes that are based on circulants. The technique carefully relocates circulants to minimize the number of short cycles. However, cycles become more detrimental when they combine together to form more advanced objects, e.g., absorbing sets, including low-weight codewords. In this paper, we show how MD relocations can be exploited to minimize the number of detrimental objects in the graph of an MD code. Moreover, we demonstrate the savings in the number of relocation arrangements earned by focusing on objects rather than cycles. Our technique is applicable to a wide variety of one-dimensional (OD) codes. Simulation results reveal significant lifetime gains in practical Flash systems achieved by MD codes designed using our technique compared with OD codes having similar parameters.